I'm unfamiliar with "First Baschee", but have done quite a few other hikes in this area.
If you are staying in Wengen, there is an easy, circular path just outside of town which leads to the beautiful view points at Mönchblick, Hunnenfluh, Leiterhorn and Staubbachbänkli. There are great views of the Eiger, Mönch, Jungfrau and the Lauterbrunnen valley.
Allmendhubel is just above Murren. From Murren, you take the Allmendhubel funicular to get there, as shown on the website you provided. There is a very short and easy "wildflower loop" at Allmendhubel itself, but my favorite hike is the "North Face Trail" from Allmendhubel back down to Murren. It's a very nice 4 mile hike, mostly downhill, which takes about 2.5 hours.
The Murren to Gimmelwald hike is very easy, along a mostly paved path. All these hikes are well marked with signs. Rick's guidebook has details about the Mannlichen-Klein Scheidegg, North Face Trail and Murren-Gimmelwald hikes. The Tourist offices in Wengen, Lauterbrunnen and Murren will have other options as well as maps.